Question

Calculate the present value of the following annuity streams: a. $4,000 received each year for 6 years on the last day of each year if your investments pay 5 percent compounded annually. b. $4,000 received each quarter for 6 years on the last day of each quarter if your investments pay 5 percent compounded quarterly. c. $4,000 received each year for 6 years on the first day of each year if your investments pay 5 percent compounded annually. d. $4,000 received each quarter for 6 years on the first day of each quarter if your investments pay 5 percent compounded quarterly. (For all requirements, do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

Answer 1

Answers:

a) PV     27,207.65

b) PV     111,152.34

c) PV   28,568.03

d) PV   112,541.74

Explanation:

The formula for an annuity present value is as follows:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

For each case we will plug the values into and solve:

A)

C 4,000

time 6

rate 0.05

$4000 \times \frac{1-(1+0.05)^{-6} }{0.05} = PV$

PV $27,207.6513

B)

C   4,000

time 24 (6 years x4 quearter per year)

rate 0.0125 (5% annual divided by 4 quearter per year)

$4000 \times \frac{1-(1+0.0125)^{-24} }{0.0125} = PV$

PV $111,152.3361

C) same as A) but being an annuity-due, whch means the payment are made at the beginning of the period:

ordinary annuity x (1+r) = annuity-due

$27,207.6513  x 1.05 = $28,568.0338

D) same procedure as C:

ordinary annuity x (1+r) = annuity-due

$111,152.3361  x 1.05 = $112,541.7403